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Weak Stability of Centred Quadratic Stochastic Operators
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.ORCID iD: 0000-0002-5816-4345
State Univ Appl Sci Elblag, Krzysztof Brzeski Inst Appl Informat, Ul Wojska Polskiego 1, PL-82300 Elblag, Poland.
Gdansk Univ Technol, Dept Probabil & Biomath, Ul Narutowicza 11-12, PL-80233 Gdansk, Poland.
2019 (English)In: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, ISSN 0126-6705, Vol. 42, no 4, p. 1813-1830Article in journal (Refereed) Published
Abstract [en]

We consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offsprings trait is equal to an additively perturbed arithmetic mean of the parents traits. It is shown that for the existence of a weak limit, it is sufficient that the distributions of the trait and the perturbation have a finite variance or have tails controlled by a suitable power function. In particular, probability distributions from the domain of attraction of stable distributions have found an application, although in general the limit is not stable.

Place, publisher, year, edition, pages
MALAYSIAN MATHEMATICAL SCIENCES SOC , 2019. Vol. 42, no 4, p. 1813-1830
Keywords [en]
Asymptotic stability; Dyadic stability; Infinite divisible distributions; Quadratic stochastic operators; Weak convergence
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-158840DOI: 10.1007/s40840-017-0575-8ISI: 000471896200032OAI: oai:DiVA.org:liu-158840DiVA, id: diva2:1337660
Note

Funding Agencies|Knut and Alice Wallenberg Foundation; Svenska Institutets Ostersjosamarbete Scholarship [11142/2013, 19826/2014, 00507/2012]

Available from: 2019-07-16 Created: 2019-07-16 Last updated: 2019-11-07Bibliographically approved

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